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Steel-concrete composite columns are strong and efficient structural members. However, their strength is not consistently recognized within design standards. In particular, current provisions regarding the strength of composite columns under combined axial compression and biaxial bending are overly simplistic and conservative. This paper presents a study of the biaxial behavior of square and rectangular, filled and encased composite columns and methods of evaluating their strength. Analyses of composite cross sections confirm the conservative nature of current design provisions and form the basis for modified strength equations that better capture the shape of the three-dimensional interaction surface. Analyses of composite columns confirm that the proposed design equations are suitable for use within the direct analysis method for evaluating members with length effects. The proposed design equations are further validated against published experimental results. This paper provides key insights on the behavior of composite columns subjected to axial compression and biaxial bending and offers an improved yet practical method of evaluating strength under these conditions that will enable more efficient designs. [ABSTRACT FROM AUTHOR]

In recent decades, there has been extensive research on the behaviour of steel structures under seismic actions. While the monotonic behaviour of steel elements subjected to uniaxial bending is well understood, there is still a need to investigate the cyclic behaviour and energy dissipation capacity, especially in relation to metal elements subjected to biaxial bending. This is of paramount interest for seismic analysis and performance assessment of steel buildings. Modelling and damage assessment criteria derived for members subjected to uniaxial bending may not be entirely appropriate for the seismic analysis of buildings composed of structural steel members subjected to biaxial bending. Therefore, this research aims to investigate the behaviour of steel members subjected to biaxial cyclic bending and compare it to behaviour under uniaxial loading conditions. To this end, detailed 3D finite element analyses are conducted to examine the effects of bidirectional lateral cyclic loading on the hysteretic response of steel members under different uniaxial and biaxial lateral displacement‐controlled load paths. The numerical results presented in this paper provide an insight into the influence of biaxial loading on the behaviour of steel members in terms of backbone curves and deformation capacity, and indicate that biaxial cyclic loading paths can significantly affect the rotation capacity of steel elements. [ABSTRACT FROM AUTHOR]

Internal forces are integrals of stress in a section area. Integrating the stress for an arbitrary cross-section shape and for the nonlinear stress-strain law σ(ε) is tedious and the use of the boundary integral approach can simplify computations. Numerical integration when applied to the computations of such integrals introduces errors in many cases. Errors of numerical integration depend on the adopted integration scheme, the type of σ(ε) and the shape of the cross-section boundary. In the case of adaptive numerical integration what is very important are the properties of the sequence of errors produced by a given integration scheme in the increasing order of the numerical quadrature or the increasing number of subdivisions. This paper analyses errors caused by different integration schemes for the typical σ(ε) either for a straight or curved boundary. Special attention is paid to the properties of the error sequence in each case. The outcome of this paper is important from the viewpoint of the reliability and robustness of the software developed for nonlinear simulations of bar structures. [ABSTRACT FROM AUTHOR]

Copyright of Revista Ingeniería e Investigación is the property of Universidad Nacional de Colombia, Facultad de Ingenieraia and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, the stressing state modeling analysis of the residual strain data of H-steel columns reveals three characteristic points that exist during the failure of H-steel columns. Also, the correctness of the stressing state analysis method, residual, and buckling characteristic pairs was verified. First, the experimental residual strains were transformed into generalized strain energy density (GSED) values as the state variables for establishing the stressing state mode and characteristic parameters (characteristic pairs). The Mann-Kendall (M-K) criterion is applied to the normalized GSED sum-j curves to reveal the characteristic points P, Q, and U of the evolving stressing state of the H-steel column. Characteristic point P is defined as the elastic-plastic branch point of the H-steel column, characteristic point Q is defined as the failure starting point, and characteristic point U is defined as the progressive failure point. Around the characteristic points of the H-steel columns, the directly modeled stressing state characteristic pairs, residual characteristic pairs, and buckling characteristic pairs produce significant mutation characteristics. This phenomenon verifies the correctness of the revealed H-steel column characteristic points and the rationality of this paper's stressing state modeling method. Then, it is proposed that the elastic-plastic branch point P can be directly used as the design reference point, and it is compared with the design point given by Code EN1993–1–5. In conclusion, this paper provides new ideas for analyzing steel structures and opens up the value of residual strain data in structural analysis.

This paper presents an analytical procedure for the design of the longitudinal reinforcement in reinforced concrete rectangular sections subjected to axial load and biaxial bending moment. The integration of the equilibrium equations is performed in analytical form for the case of uniaxial moment, including the effect of the reinforcement placed on the sides of the section and adopting code‐based constitutive laws for steel and concrete. The strength domain of the section is calculated in closed form for the case of only main steel and in simplified form when including the reinforcement disposed on the side. Additionally, a formulation is proposed for the interaction domain of the two components of the bending moment for constant axial load, in which the uniaxial moment capacities are calculated including all the rebars within the section. The proposed method is adopted for setting a design procedure of the steel bars of rectangular sections subjected to biaxial bending. Comparisons with numerical results and code provisions show the reliability of the approach, which reduces computational costs and give useful indications for practitioners and designers. [ABSTRACT FROM AUTHOR]

Concrete exposed to fire can experience spalling when the pore pressure increases due to water evaporation resulting in damage to part of the concrete cross-section which causes the loss of the initial cross-sectional symmetry, both thermal and geometrical. This may lead to what is, in essence, a biaxial bending problem in reinforced concrete columns. This study does not deal with the prediction of the occurrence of spalling for which a fully coupled hygro-thermo-mechanical analysis would be required. This work evaluates the consequences that corner spalling and surface spalling have on the fire resistance of reinforced concrete columns and presents a methodology based on the determination of a modified fire resistance time. An advanced fiber based numerical model for evaluating the fire resistance of RC sections exposed to fire is used as a tool to analyse the effect that spalling has on the performance of the columns. The model is able to generate the interaction surfaces of the columns subjected to uniaxial or biaxial bending and 4-sided exposed to the standard fire curve ISO 834. After a parametric analysis, it is observed that the negative effect of spalling can be quantified by means of an additional fire exposure time, which ranges between 0–35 min and depends on the column cross-section configuration, dimensions and load level. Finally, a proposal for the calculation of the modified fire resistance time for the effect of spalling is presented, which may be beneficial for practitioners in design. [ABSTRACT FROM AUTHOR]

Featured Application: This study is a practical tool for Structural Engineers to obtain the minimum contact area with the ground for rectangular isolated footings with an eccentric column. This manuscript aims to present a novel model to find the optimal area of a rectangular isolated footing with an eccentric column, taking into account that the footing is partially supported; that is, one part of the contact surface is compressed and the other part has zero pressure. The methodology is developed by integration and can also be verified using the geometric properties of a triangular-based pyramid to determine the axial load, the moments in the X and Y axes in terms of the available allowable soil pressure, the footing sides, the greatest distance on one of its sides in the X-direction where it crosses the neutral axis, the greatest distance on one of its sides in the Y-direction where it crosses the neutral axis, and the coordinates at the base of the footing. Four types of numerical problems are shown to find the optimal area of a rectangular footing with an eccentric column subjected to biaxial bending: (1) the column in the center of the footing; (2) the column on the edge of the footing in the X-direction; (3) the column on the edge of the footing in the Y-direction; and (4) the column in the corner of the footing. A comparison is presented of the new model against a model proposed by another author. The new model presents a reduction of up to 42.37% for the column in the center of the footing and up to 40.32% for the column in the corner of the footing compared to the model by the other authors. Therefore, the new model will be of great help to professionals in foundation design. [ABSTRACT FROM AUTHOR]

A testing research on the local-biaxial flexural interactive buckling of high strength steel Q460C, Q550D and Q690D welded box slender section beam-columns subjected to combined compression force and biaxial bending is reported. A total of thirteen median long steel columns, of which four manufactured from Q460C steel, five from Q550D steel and four from Q690D steel, were loaded until failure under biaxial eccentric compression forces. The local-biaxial flexural interaction buckling behavior is investigated by analyzing the test results. As an addition to the test data, the finite element parameter analyses are performed. The ultimate bearing capacities obtained from the test in this study and the numerical results presented in this study or in the existent literatures are compared with the calculation results in accordance with the design methods recommended in the American Specification ANSI/AISC 360–16, Eurocodes BS EN 1993-1-1 and BS EN 1993-1-5, and the newly proposed Effective Yield Strength Method (EYSM) and Effective Section Method (ESM) to check whether the current technical provisions and the new methods are suitable to the high strength steel beam-columns examined in this paper. The experimental and numerical results show that after taking the resistance factor into account, the ANSI/AISC 360–16, EN 1993-1-1 and BS EN 1993-1-5 are very conservative for the high strength steel beam-columns with greater member slenderness ratios (λ = 80, 90, 100) or with smaller plate width-to-thickness ratios (square box sections with b/t = 40, or rectangular box sections with h/t = 40 or b/t = 17); the new proposed EYSM provides an excellent prediction of the ultimate bearing capacities of the beam-columns and thus suitable for the high strength steels; but the new proposed ESM gives a very conservative estimate, over the range of steel nominal yield stress f y = 460 MPa ∼ 690 MPa, plate width-to-thickness ratio b/t = 40–80, member slenderness ratio λ = 40–100. • A testing research on the local-biaxial flexural interactive buckling of high strength steel welded box slender section beam-columns subjected to combined compression force and biaxial bending is reported. The local-biaxial flexural interaction buckling behavior is investigated. • The ultimate bearing capacities obtained from the test in this study and the numerical results presented in this paper or in the existent literatures are compared with the calculation results in accordance with the design methods recommended in the American Specification ANSI/AISC 360–16, Eurocodes BS EN 1993-1-1 and BS EN 1993-1-5, and the newly proposed Effective Yield Strength Method (EYSM) and Effective Section Method (ESM) to check whether the current technical provisions and the new methods are suitable to the high strength steel beam-columns examined. • The experimental and numerical results show that after taking the resistance factor into account, the ANSI/AISC 360–16, EN 1993-1-1 and BS EN 1993-1-5 are very conservative for the high strength steel beam-columns with greater member slenderness ratios (λ = 80, 90, 100) or with smaller plate width-to-thickness ratios (square box sections with b/t = 40, or rectangular box sections with h/t = 40 or b/t = 17); the new proposed EYSM provides an excellent prediction of the ultimate bearing capacities of the beam-columns and thus suitable for the high strength steels; but the new proposed ESM gives a very conservative estimate, over the range of steel nominal yield stress f y = 460 MPa ∼ 690 MPa, plate width-to-thickness ratio b/t = 40–80, member slenderness ratio λ = 40–100. [ABSTRACT FROM AUTHOR]

Copyright of Beton- Und Stahlbetonbau is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The aim of this article is to describe problems of members subjected to biaxial bending and axial compression force and the methods of their design. Members subjected to bending moments about two axes and axial compression force exhibit complex behavior. It is necessary to consider second order theory and imperfections when designing members like that, since they have noticeable influence on resistance in instability. There are examples shown in the article, using methods present in current European standards EN 1993-1-1 and EN 1999-1-1. Attention is drawn to differences in methods, both in applicability and practicality, in design of members with constant and linear bending moment. The purpose of presented paper is to show if the method, which is currently used in Eurocode for aluminum structures, can be also used for steel structures. [ABSTRACT FROM AUTHOR]

Copyright of Mauerwerk is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Reinforced concrete (RC) structural members, such as bridge girders and columns, flanged and spandrel beams, and edge frame beams, may be subjected to combined actions in the general case of loading. Despite extensive research on the behavior of RC members strengthened with fiber-reinforced polymer (FRP) composites under pure actions, questions have been raised about the strengthened RC members subjected to combined actions, particularly actions including torsion. As a contribution to this demanding field of research, the first theoretical model capable of predicting the full load–deformation response of RC members strengthened with conventional FRP-strengthening configurations, and subjected to torsion combined with biaxial bending, was developed based on the principles of the well-known combined-actions softened truss model (CA-STM). The proposed model considered the influence of various parameters, such as FRP stiffness, on the constitutive laws of materials. In addition, the computational operations and duration were significantly reduced, and the numerical stability of the solution procedure was enhanced by extending the refined efficient solution algorithm for FRP-strengthened RC members for the first time. Furthermore, the efficiency and contribution of the FRP system and the governing failure mode was accurately predicted. Three categories of equations, including equilibrium equations, compatibility equations, and the constitutive relationships of materials, were incorporated into the proposed model, then a system of 16 nonlinear equations, containing 16 unknown variables, was solved to obtain the full load–deformation response of an FRP-strengthened member subjected to combined actions, including torsion. A detailed comparison conducted between the test results of a database with various strengthening patterns collected from the literature and the predictions of the proposed model showed that the model was able to estimate the ultimate strength, with a mean value and coefficient of variation of 1.11% and 13%, respectively, in addition to predicting the overall load–displacement response well. This research highlights the importance of considering the combined effects of bending and torsion on the capacity of fiber-reinforced polymer (FRP)-strengthened reinforced concrete (RC) members, particularly in members where torsion is critical. The addition of flexural moment in certain situations can lead to a reduction in the torsional capacity of the member's cross-section. While in specific situations, where the strengthening system is asymmetrically applied or the internal steel arrangement of the section is asymmetrical, the torsional capacity can even increase compared to the case when subjected to pure torsion. Therefore, the arrangement of the strengthening system plays a crucial role in determining the failure mode and strength of the member. The model proposed in this study, along with its resulting findings, will provide valuable assistance to engineers in determining the optimal percentage of an FRP system and its pattern in these situations. This will allow them to achieve the highest possible effectiveness of the strengthening system in cases involving combined actions, including torsion and flexure. [ABSTRACT FROM AUTHOR]

This study introduces the Failure Decision Function, a novel approach for evaluating the structural capacity of rectangular reinforced concrete columns under axial forces and moments, both uniaxial and biaxial. The method simplifies existing practices, enhancing accuracy and integration into design software. The methodology hinges on deriving exact biaxial bending failure surfaces, utilizing integral expressions based on material properties and cross-sectional geometry. This direct integration process uncovers failure surface characteristics previously undocumented. Results confirm the utility of the Failure Decision Function through comparative analysis with established literature, showcasing its potential for simplifying and improving structural capacity assessments. The analytic procedure developed enables efficient computation of failure surfaces, streamlining the inclusion of these functions in structural engineering software in two key ways: (1) compiling a library of pre-calculated functions for quick capacity checks and (2) creating a dynamic application that generates these functions based on specific design parameters, allowing users to explore various load and moment scenarios. In conclusion, the Failure Decision Function represents a significant advancement in structural engineering design, offering an accurate and user-friendly method for assessing column performance under critical loading conditions. [ABSTRACT FROM AUTHOR]

Available capacity models for the assessment of seismic capacity of RC columns are mainly based on experimental tests under axial load and uniaxial bending. Furthermore, experimental tests have been mainly performed on columns representative of new constructions. To analyze the effects of biaxial bending on the seismic performances of existing RC columns with design characteristics nonconforming to present day seismic codes and practices, this paper presents the results of a first stage of tests on RC columns under both axial load and biaxial bending, which effectively simulate the seismic actions. In particular, this paper presents results of four tests on full-scale square columns reinforced with plain bars subjected to constant axial load and biaxial cyclic actions. Two different cyclic displacement paths were investigated: horizontal displacements with an inclination angle of 45 or 30°, with respect to the cross-section principal axes. The influence of biaxial bending actions on the global behavior of existing RC columns in terms of stiffness, strength, deformation capacity, and the effects of different horizontal displacements orientation on their performances are herein investigated and discussed; the comparison with experimental outcomes provided by uniaxial bending tests on companion specimens are also presented. Experimental findings showed that biaxial bending actions affect columns rotational capacity more than strength. The rotational capacity reduction because of biaxial bending actions, even if more significant than the flexural capacity reduction, is not currently taken into account in the available seismic guidelines related to existing RC buildings. [ABSTRACT FROM AUTHOR]

A simplified analytical method that determines the axial load and biaxial moment capacities of a rigid spread footing of regular or arbitrary shape resting on soil is presented. Three different types of pressure distribution at the soil-footing interface are considered: uniform, linear, and parabolic. The proposed algorithm can be used to determine (1) the maximum soil-bearing stress under rigid spread footings subjected to vertical load and biaxial bending moments; (2) the vulnerability of exceeding the maximum soil-bearing stress by comparing the biaxial moment-axial load interaction diagrams of the footing with those of the attached wall or column; and (3) the development of nomograms for the analysis and design of spread rigid footings of different shapes. Three comprehensive examples are included that show the first two applications. The third application is shown in a companion paper that deals with development of design aids for the analysis and design of rectangular and trapezoidal spread footings. [ABSTRACT FROM AUTHOR]

Design aids (nomograms) for rectangular and symmetrical trapezoidal rigid spread footings are developed using a method previously developed by the writers in a companion paper. The nomograms can be used by designers to directly determine their maximum axial load and biaxial moment capacities without exceeding the bearing capacity of the supporting soil. Three different types of pressure distribution at the soil-footing interface are considered: uniform, linear, and parabolic. The results obtained can then be compared with the biaxial moment-axial load interaction diagrams of the attached concrete walls or columns. This allows the structural designer to determine the vulnerability and likelihood of exceeding the bearing capacity of the supporting soil. Four examples are presented that show the effectiveness and simplicity of the proposed nomograms in the analysis of isolated rectangular and trapezoidal rigid spread footings resting on soil. [ABSTRACT FROM AUTHOR]

This paper presents a design procedure for braced high-strength reinforced concrete columns under the action of uni-axial and biaxial loading. The paper has two phases; the first phase represents the design procedure of such columns under the action of uniaxial bending, while the second phase shows the implementation of the design procedure on the columns under biaxial bending. Due to the lack of uniformity in the conceptual treatment of the upper slenderness limit for short columns in different codes and the unclear definition of the maximum slenderness limit for slender columns as well, a new approach has been presented. Proposed expressions for the flexural rigidity have been presented based on the mode of failure of such columns. In addition, the equivalent column concept has been implemented to reduce the uni-axially loaded column to an axially loaded one, hence, the upper slenderness limit for the short column condition can be checked properly. As a consequence, a design procedure for the uniaxially loaded column is presented using a strength interaction diagram. Furthermore, the adequacy of the proposed procedure for predicting the second order effect has been verified against the experimental results. The same proposed design procedure in the first phase has been implemented in each direction of the column cross -section then the load contour equation can be used to check the strength of such column under biaxial loading. Finally, two worked examples have been presented covering different curvature modes: single and double. The proposed design procedure shows its competence against the experimental test results and well-designed columns according to the provisions of the current codes as ECCS 203-2001 and ACI 318-05 for braced systems. [ABSTRACT FROM AUTHOR]

This paper presents the effects of various amounts of steel fibers on the behaviour of eccentrically loaded high strength reinforced concrete columns. A total of 14 both short and slender square section steel fiber and plain high strength reinforced concrete column specimens were constructed and tested to investigate the addition of steel fibers on load–deflection behaviour, ultimate strength capacity, ductility and confinement. The complete nonlinear experimental stress–strain relationships of steel fiber and plain high strength concrete were obtained for different concrete strengths. In the study, a theoretical procedure considering the nonlinear behaviour of the materials is proposed for ultimate strength analysis and load–deflection behaviour of eccentrically loaded columns including slenderness effect. The complete experimental and theoretical biaxial load–deflection curves of the column specimens have been obtained and reported in the paper. The column specimens and some steel fiber columns available in the literature have been analysed for the ultimate strength capacities. Good agreement has been achieved between the analysis and the test results. [ABSTRACT FROM AUTHOR]

The loads applied to angle beams usually act out of the principal planes so that they cause simultaneous biaxial bending about both principal axes. The general practice for designing unbraced beams against biaxial bending is to consider the separate failure modes of either in-plane bending or lateral buckling under bending about the major principal axis, and in-plane bending about the minor principal axis, and then to use an interaction equation to combine the two principal axis strengths. However, the interaction equations provided by many codes for designing against biaxial bending are largely derived from research on doubly symmetric I-section beams, which may be inappropriate for angle section beams, while the lateral buckling rules of these codes appear to be in error for nonuniform bending with loads acting away from the shear center. This paper investigates the biaxial bending of unbraced steel angle beams. The biaxial bending of compact equal angles in uniform bending is considered first, and a simple interaction equation is developed for their design which utilizes recent proposals for lateral buckling design. A corresponding interaction equation is developed for the design of semicompact and slender equal angles. Suggestions are then made for extending these to the biaxial bending of unequal angles under general shear center loading, and finally, a worked example illustrating the method is provided. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to establish a complete analytical solution concerning the linear pressure distribution under rigid rectangular spread footings. An eccentricity diagram is developed to map the unique footing deformations and compression zones in each one of five distinct regions. For each region, the linear soil pressure, neutral axis position, and pressure values at the four corners are expressed in closed forms. The accuracy and consistency of the explicit expressions are verified by presenting several special boundary cases, whereas the physical interpretation is brought out by analyzing the eccentricity diagram. A generic nomogram providing the maximum soil pressure is also formed to promote efficient structural footing design. The developed analytical formulas for responses and resultants enable algorithmic implications without iterations and offer high computational efficiency. Proper examples, generated via developed computer software, exhibit how the theoretical content of this article is applied in practice. The software enables three-dimensional (3D) viewing of the deformed and undeformed physical and mathematical model of the structure, allowing detailed visual inspection of the results. [ABSTRACT FROM AUTHOR]

This paper presents a new computer method for moment-curvature analysis of arbitrary-shaped composite steel-concrete cross-sections that are subjected to biaxial bending and axial force. The complete moment-curvature diagrams are determined such that axial force and bending moment ratio is kept constant. A strain-driven algorithm has been developed, the solution of the nonlinear equilibrium equations is controlled by the assumed strain values in the most compressed point and by solving just two coupled nonlinear equations. Such an approach may be used to assess accurately the main features of the elasto-plastic behaviour of composite cross-sections: multiple yielding points associated to different materials, flexural and axial rigidity, moment-curvature relationship in pre and post-critical domain and curvature ductility detecting also unloaded regions of the cross-sections that may occur even under monotonically increasing of the total bending moment. Since the Jacobian’s of the resulted nonlinear system of equations is always positive definite the convergence stability is not sensitive to the initial/starting values of the iterative process and to the strain softening exhibited by the concrete in compression. By using a path integral technique on boundary of cross-section area, gradual spread of plasticity and residual stress distribution assumed for encased steel elements are accurately considered reducing also the computational time significantly. In order to illustrate the proposed method and its accuracy and efficiency, a computer program has been developed and used to study several representative examples. The numerical studies presented and comparisons made prove the effectiveness and time saving of the proposed method of analysis. [ABSTRACT FROM PUBLISHER]

For design situations in case of ambient temperature, both EN1992-1-1 and ACI318 provide guidelines for the design of columns, and for evaluating the structural capacity in case of biaxial bending. However, the effect of fire on these columns subjected to biaxial bending is not mentioned in the provisions. Hence, it is important to evaluate the mechanical behavior of columns in case of biaxial bending combined with fire and to provide guidelines for fire resistance design. In this paper, first a simplified method proposed by Bresler is presented for design under ambient temperature in order to predict the interaction curves of concrete columns subjected to biaxial bending and axial loading, based on a calculation of the uniaxial bending capacity. In order to verify whether this method can be adopted in case of fire, a cross-sectional calculation tool is introduced and validated with experimental data. Further, the results from the simplified method are compared with those obtained with the calculation tool. Subsequently, the simplified method is elaborated further in order to take into account the effect of an ISO 834 standard fire for a column loaded by a symmetrical biaxial load. Finally, the results of a parametric study are presented. Suggestions are given for implementing this method for design of relatively short concrete columns subjected to biaxial bending in case of an ISO 834 fire. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive experimental and numerical investigation on hysteretic behavior of thin-walled circular steel tubes as loaded members in reticulated shells. The experimental setup available for constant compression and biaxial bending loading was designed to examine the failure process, failure modes, load bearing capacity, ductility, stiffness degradation and energy dissipation capacity of sixteen thin-walled circular steel tubes. Also, the effects of the loading condition, axial load ratio, slenderness and steel strength on hysteretic behavior of specimens were investigated. The study showed that test results of specimen loaded in two directions might overestimate hysteretic characteristic of this member. Premature local buckling may be caused by the high axial load ratio and the recommended axial load ratio may be n ≤ 0.2 to ensure the load bearing capacity, deformation capacity and ductility of circular steel tubes and to prevent the premature local buckling occurring in engineering practice. Slenderness affects the load bearing capacity, ductility, and energy dissipation capacity of specimens, and with an increasing slenderness, the stiffness degraded considerably and quickly. Specimens with high strength steel exhibited higher load bearing capacity and better stiffness but lower energy dissipation capacity than those made by low strength steel. Furthermore, the nonlinear finite element analysis was performed to simulate hysteretic behavior of test specimens, and the results got a satisfactory agreement with those of test. [ABSTRACT FROM AUTHOR]

Biaxially loaded high strength rectangular concrete-filled steel tubular (CFST) slender beam-columns with large depth-to-thickness ratios, which may undergo local and global interaction buckling, have received very little attention. This paper presents the verification of a multiscale numerical model described in a companion paper and an extensive parametric study on the performance of high strength thin-walled rectangular CFST slender beam-columns under biaxial loads. Comparisons of computer solutions with existing experimental results are made to examine the accuracy of the multiscale numerical model developed. The effects of the concrete compressive strength, loading eccentricity, depth-to-thickness ratio and columns slenderness on the ultimate axial strength, steel contribution ratio, concrete contribution ratio and strength reduction factor of CFST slender beam-columns under biaxial bending are investigated by using the numerical model. Comparative results demonstrate that the multiscale numerical model is capable of accurately predicting the ultimate strength and deflection behavior of CFST slender beam-columns under biaxial loads. Benchmark numerical results presented in this paper provide a better understanding of the local and global interaction buckling behavior of high strength thin-walled CFST slender beam-columns and are useful for the development of composite design codes. [ABSTRACT FROM AUTHOR]

This paper deals with the analytical proof of the equivalence between the relative biaxial bending resistance of a rectangular solid reinforced concrete section and the biaxial bending resistance of the transformed solid square section of unit-length side. Similar proofs are also derived for rectangular hollow sections. The results of the analytical proof show that the relative biaxial bending resistance of a rectangular solid section is identical to the biaxial bending resistance of the transformed square solid section of unit-length side. These results only occur when the concrete fiber and reinforcing bar coordinates in the transformed section are in conformity with the transformation that maps the rectangular section into a square cross section of unit-length side. The concrete and steel stresses in the transformed section comply with the resulting stress transformation and the area of reinforcement in the transformed section must comply with the resulting area transformation. The proof also shows the equivalence in rectangular hollow sections, provided that similar transformation-related conditions are met. [ABSTRACT FROM AUTHOR]

Copyright of Revista Ingeniería e Investigación is the property of Universidad Nacional de Colombia, Facultad de Ingenieraia and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Abstract: The steel tube walls of a biaxially loaded thin-walled rectangular concrete-filled steel tubular (CFST) slender beam-column may be subjected to compressive stress gradients. Local buckling of the steel tube walls under stress gradients, which significantly reduces the stiffness and strength of a CFST beam-column, needs to be considered in the inelastic analysis of the slender beam-column. Existing numerical models that do not consider local buckling effects may overestimate the ultimate strengths of thin-walled CFST slender beam-columns under biaxial loads. This paper presents a new multiscale numerical model for simulating the structural performance of biaxially loaded high-strength rectangular CFST slender beam-columns accounting for progressive local buckling, initial geometric imperfections, high strength materials and second order effects. The inelastic behavior of column cross-sections is modeled at the mesoscale level using the accurate fiber element method. Macroscale models are developed to simulate the load-deflection responses and strength envelopes of thin-walled CFST slender beam-columns. New computational algorithms based on the Müller''s method are developed to iteratively adjust the depth and orientation of the neutral axis and the curvature at the column''s ends to obtain nonlinear solutions. Steel and concrete contribution ratios and strength reduction factor are proposed for evaluating the performance of CFST slender beam-columns. Computational algorithms developed are shown to be an accurate and efficient computer simulation and design tool for biaxially loaded high-strength thin-walled CFST slender beam-columns. The verification of the multiscale numerical model and parametric study are presented in a companion paper. [Copyright &y& Elsevier]

• Monitoring biaxial bending structural deformations by optical fiber. • An improved conjugate beam method is proposed to calculate the deflection. • An algorithm is established by BP neural network to calculate the deflection. • Taking a concrete simple beam test to verify the above two methods. Concrete structures are often subjected to loads in both directions, resulting in deflections in both directions. To comprehensively and automatically monitor these continuous deformations, this paper uses a distributed optical fiber to monitor the strain of a structure and establishes the strain-deflection relationship by both an improved conjugate beam method and a BP neural network. The improved conjugate beam method applies to simple structures, such as simple beams, and the BP neural network applies to complex structures. A concrete simple beam model is used to verify the two methods. The results show that the relationships between the strain and deflection that are established by the two methods have high precision, and the results of the BP algorithm are closer to the actual deflections than the results of the explicit function method. [ABSTRACT FROM AUTHOR]

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Copyright of Revista Sul-Americana de Engenharia Estrutural is the property of Revista Sul-Americana de Engenharia Estrutural and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Laterally and torsionally unrestrained steel I-section beams are susceptible to torsional deformations between supports; therefore, according to Part 1-1 of Eurocode 3, they need to be designed to resist lateral-torsional buckling. Eurocode's steelwork design criteria require safety checking based on two stability interaction formulae utilizing the so-called equivalent uniform moment factors and the cross-section resistance formula that, in the case of moment gradient, refer to the beam end section. Uncoupling the beam stability resistance criterion and the cross-section resistance criterion may result in a nonuniform safety assessment of I-section beams. Finite element simulations of the beam resistance for different moment gradient ratios are performed. Verification of the buckling resistance is conducted by varying the following parameters: the slenderness ratio, the location of maximum end moments about both axes and the section depth-to-width ratio (i.e., considering rolled I- and H-sections). The variation in the accuracy of the current Eurocode resistance evaluation method is identified, and an approach for a better equalization of the safety predictions is suggested by considering different values of the most important factors influencing the stability performance of steel I-section beams. [ABSTRACT FROM AUTHOR]

Reinforced concrete (RC) columns, when exposed to fire, are often subjected to biaxial bending arising from eccentricity in loading or one-, two-, and three-sided exposure or due to nonuniform spalling. The effect of such biaxial bending is often not taken into consideration in evaluating the fire resistance of RC columns. In this paper, an approach is presented for modeling the fire response of RC columns under biaxial bending. This approach accounts for high-temperature material properties, geometric and material nonlinearity, fire-induced spalling, and restraint effects and can be applied under realistic fire and loading scenarios. The validity of the approach is established by comparing the predictions from the model with results from full-scale fire resistance tests. The model is applied to undertake a set of parametric studies and the results show that the biaxial bending effect arising from one-sided, two adjacent-sided, and three-sided fire exposure significantly decreases the fire resistance of RC columns. [ABSTRACT FROM AUTHOR]

Abstract: Most design codes (Model Code 90, ACI-318-2008 and Eurocode–2-2004) suggest that the effect of a geometrical imperfection ought to be taken into account in the most unfavorable direction when designing slender reinforced concrete columns. If the bending plane of the beam–column is related to the strong axis, this imperfection acting in the opposite direction results in the column being subjected to axial load and biaxial bending, complicating the design procedure and increasing computational costs considerably. Such standards do not indicate when this geometrical imperfection generates a notable loss of resistance in the column. This paper proposes the geometrical slenderness of the weak axis as the variable that determines whether or not to consider the influence of such imperfection. This paper denominates this boundary value the “slenderness limit of the weak axis” (), and this is associated with a loss of resistance of 10% of the bending moment of the unbraced columns with respect to non-sway columns. An approximated equation of this limit is proposed using the results of a numerical simulation. The equation is valid for rectangular columns with doubly symmetric reinforcement and both normal and high strength concrete, and also for short-term and sustained loads. [Copyright &y& Elsevier]

This paper presents an analytical model for prediction of the load carrying capacity of reinforced concrete (RC) columns confined with carbon fiber reinforced polymers (CFRP) under uniaxial and biaxial eccentric loading. The model is based on realistic material laws and accounts for the non-linear stress-strain behavior of both unconfined and CFRP-confined concrete. Under uniaxial eccentric loading, the column cross-section is discretized into finite layers along the section depth. For a symmetric square cross-section subjected to biaxial eccentric loading with equal eccentricity about each principal axis, the column cross-section is discretized into finite layers along the diagonal of the column cross-section. For a given strain distribution in a direction perpendicular to the neutral axis, the sectional forces are integrated numerically and the load capacity of the column is predicted using an iterative process. For rectangular and non-symmetric square cross-sections subjected to biaxial eccentric loading, the load capacities under uniaxial eccentric loading along each principal axis are first derived independently. The column load capacity under concentric axial loading is calculated. The determined distribution of the column load capacities under uniaxial eccentric loading and concentric loading are then utilized to compute the load capacity under biaxial eccentric loading using the reciprocal load equation. An experimental study was carried out to examine the effectiveness of the CFRP-confinement to improve the load capacity and ductility of RC columns under biaxial eccentric loading. The accuracy of the proposed analytical model was demonstrated by comparing the model predictions to results of the current experimental study in addition to experimental data published in the literature. [ABSTRACT FROM AUTHOR]

The paper presents a method and an integration procedure specifically targeting the analysis of cross sections under biaxial bending and axial load, whatever the shape- including internal voids-and made of different materials (for example, concrete) internally or externally reinforced by mild steel, prestressing tendons, and fiber-reinforced polymers. Surface integration of meshed cross sections allows moment-curvature relationships to be computed using nonlinear constitutive relationships (also with softening) and three- dimensional (3D) interaction domains P-Mx-My to be drawn. Iteration procedures and convergence criteria are herein proposed to rapidly solve the highly nonlinear problem. Numerical tests showed fast convergence of the algorithm and good agreement with experimental results elsewhere; comparisons between the numerical outcomes and the simplified expressions available in the literature have been performed to point out the current limits of the available codes' formulas. [ABSTRACT FROM AUTHOR]

Abstract: The theory and algorithms of a performance-based analysis (PBA) technique for the nonlinear analysis and performance-based design of thin-walled concrete-filled steel tubular (CFST) beam–columns with local buckling effects were presented in a companion paper. Initial local buckling and effective strength/width formulas for steel plates are incorporated in the PBA program to account for local buckling effects. Performance indices are used in the PBA program to quantify the section, axial ductility and curvature ductility performance of thin-walled CFST beam–columns. This paper presents the verification and applications of the PBA program developed. The axial load–strain curves, ultimate axial loads and moment–curvature curves for thin-walled CFST columns predicted by the PBA program are verified by experimental data. The PBA program is then utilized to investigate the effects of local buckling, depth-to-thickness ratio, concrete compressive strengths, steel yield strengths and axial load levels on the stiffness, strength and ductility performance of thin-walled CFST beam–columns under axial load and biaxial bending. The PBA technique developed is shown to be efficient and accurate and can be used directly in the performance-based design of thin-walled CFST beam–columns and implemented in advanced analysis programs for composite columns and frames. [Copyright &y& Elsevier]

Abstract: This paper presents a performance-based analysis (PBA) technique based on fiber element formulations for the nonlinear analysis and performance-based design of thin-walled concrete-filled steel tubular (CFST) beam–columns with local buckling effects. Geometric imperfections, residual stresses and strain hardening of steel tubes and confined concrete models are considered in the PBA technique. Initial local buckling and effective strength/width formulas are incorporated in the PBA program to account for local buckling effects. The progressive local buckling of a thin-walled steel tube filled with concrete is simulated by gradually redistributing normal stresses within the steel tube walls. Performance indices are proposed to quantify the section, axial ductility and curvature ductility performance of thin-walled CFST beam–columns under axial load and biaxial bending. Efficient secant algorithms are developed to iterate the depth and orientation of the neutral axis in a thin-walled CFST beam–column section to satisfy equilibrium conditions. The analysis algorithms for thin-walled CFST beam–columns under axial load and uni- and biaxial bending are presented. The PBA program can efficiently generate axial load–strain curves, moment–curvature curves and axial load–moment strength interaction diagrams for thin-walled CFST beam–columns under biaxial loads. The proposed PBA technique allows the designer to analyze and design thin-walled CFST beam–columns made of compact or non-compact steel tubes with any strength grades and normal and high-strength concrete. The verification and applications of the PBA program are given in a companion paper. [Copyright &y& Elsevier]

This paper reports an experimental investigation of the behaviour of concrete-encased composite columns subjected to short-term axial load and biaxial bending. In the study, six square and four L-shaped cross section of both short and slender composite column specimens were constructed and tested to examine the load-deflection behaviour and to obtain load carrying capacities. The main variables in the tests were considered as eccentricity of applied axial load, concrete compressive strength, cross section, and slenderness effect. A theoretical procedure considering the nonlinear behaviour of the materials is proposed for determination of the behaviour of eccentrically loaded short and slender composite columns. Two approaches are taken into account to describe the flexural rigidity (EI) used in the analysis of slender composite columns. Observed failure mode and experimental and theoretical load-deflection behaviour of the specimens are presented in the paper. The composite column specimens and also some composite columns available in the literature have been analysed and found to be in good agreement with the test results. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a comparative study of different integration methods of stresses (both analytical and numerical) for concrete sections subjected to axial loads and biaxial bending. Such methods are applied to circular and rectangular sections. The constitutive equation used is a parabola-rectangle from the Eurocode-2. The comparison was performed with regard to the accuracy and the computational speed of each method. The objective of the paper is to determine which of the integration methods compared is more efficient in computing the interaction surfaces for rectangular and circular sections. The analytical method proposed by Barros et al. [Barros MHFM, Barros A, Ferreira C. Closed form solution of optimal design of rectangular reinforced concrete sections. Eng Comput 2004;21(7):761–76] for rectangular sections is compared with the numerical method termed “modified thick layer integration” proposed by Bonet et al. [Bonet JL, Romero ML, Miguel PF, Fernandez MA. A fast stress integration algorithm for reinforced concrete sections with axial loads and biaxial bending. Comput Struct 2004;82(2–3):213–25] and with the well-known fiber method. Furthermore, two new methods are proposed for circular sections: one analytical and one numerical based on the Gauss–Legendre quadrature. The results of both methods are compared with the classical layer decomposition method. [Copyright &y& Elsevier]

Exposed-type steel column bases are used widely in low-rise building construction Numerous researchers have examined methods to identify their stiffness and strength, but those studies have heretofore been restricted to in-plane behaviors This paper presents an experimental investigation of inelastic behaviors of square hollow section (SHS) steel column bases under biaxial bending Two types of failure modes are considered anchor bolt yielding and base plate yielding Different pinching effects and interaction surfaces for biaxial bending are observed for these two modes during bi-directional quasi-static cyclic loading tests Differences are elucidated using limit analyses based on a simple analytical model [ABSTRACT FROM AUTHOR]

This paper proposes an analytical approach to calculating failure surfaces in rectangular reinforced concrete cross sections with symmetrical reinforcement when submitted to axial loads and biaxial bending. The analytical method is valid for concrete with a strength of between 25 and 80 MPa. The failure surface is obtained by means of reference generatrices that lie on two directrices corresponding to two known axial loads and on the maximum and minimum axial capacity of the section. The proposed expression was assessed with results obtained from experimental tests (from the literature) and from a numerical model. This approach enables the section capacity to be verified and the reinforcement designed to a sufficient degree of accuracy for everyday professional practice. The method is easy to use and may be extensively applied to reinforced concrete columns in buildings. [ABSTRACT FROM AUTHOR]

This paper presents one of the two new proposals for beam-column interaction formulae, which will be made available in the forthcoming EN version of Eurocode 3. It is based on second-order in-plane elasticity, and has been derived in order to exhibit an understandable physical background, as well as accuracy and consistency with the other resistance and stability formulae of the code. The formulae ensure all the required continuities: between the cross-section classes, from plasticity to elasticity when slenderness and axial force are increasing, and continuity between all the individual stability member checks and cross-section verifications. The paper shows how the basic format may be extended to cover a wider range of cases, i.e. spatial elastic–plastic behaviour with possible lateral–torsional buckling. Through an extensive comparison with the results of FEM numerical simulations of about 15 000 beam-columns, the proposal is found to be safe and accurate. [Copyright &y& Elsevier]

This paper presents a general formulation for the analysis of reinforced concrete frames. The model has been developed within the framework of lumped damage mechanics. This is a theory based on the methods of continuum damage mechanics, fracture mechanics and the concept of plastic hinge. The paper also describes the numerical implementation of the model in the finite element programs. The model is evaluated by the numerical simulation of three tests reported in the literature. Two of them deal with a column subjected to variable axial loads and biaxial flexure. The third is a two-story three-dimensional frame subjected to earthquake loadings outside the principal directions of the frame. [Copyright &y& Elsevier]

This paper presents the results of a large parametric study concerning the evaluation of the critical local buckling coefficient for thin-walled rectangular hollow section (RHS) members subjected to combined axial load and biaxial bending, accounting for web-flange interaction. The calculation of the half-wavelength leading to the minimum critical local bifurcation load is performed by means of a Generalized Beam Theory specialization, which makes it possible to quickly solve a large set of cases. In particular, taking advantage of the small half-wavelength of local buckling, it is assumed that the stresses are uniformly distributed along the member length, making it possible to resort to semi-analytical solutions using sinusoidal half-wave amplitude functions for the GBT cross-section deformation modes. On the basis of the results obtained, the key parameters governing local buckling are identified, leading to easy-to-use charts and closed-form formulae to determine the local buckling coefficient. [ABSTRACT FROM AUTHOR]

This paper presents the reliability assessment of reinforced concrete (RC) columns subjected to biaxial bending using the advanced first-order second-moment reliability method. The strength of an RC column under the biaxial bending condition is estimated by the load contour, which is utilized as the limit state function in the reliability analysis. The random variables include the strength parameters of the RC columns, the load parameters and the eccentricities of axial force. The Hasofer-Lind-Rackwitz-Fiessler algorithm with the gradient projection method is employed to calculate the most probable failure point and the reliability index. The surface exponents of the load contours are determined by the values presented by Bresler. The cubic spline interpolation is adopted to construct P-M interaction diagrams for uniaxial bending about the principal axes that are required in the load contour method. The sensitivities of the limit state function are calculated through the direct differentiation method. The reliability indices are calculated for a rectangular section and a square section. The effect of the surface exponent on the results of the reliability analysis is investigated for the rectangular section, and the uncertainty of the eccentricity of axial force is considered in the example for the square section. [ABSTRACT FROM AUTHOR]

• The local buckling of steel corrugated-plates is considered in the load-carrying capacity. • The moment capacity is evaluated based on the plastic stress distribution. • Simplified interaction equations with good accuracy are proposed. • The interaction curves of biaxial bending are almost exclusively related to the axial compression ratio. This paper studies the load-carrying capacity of concrete-infilled double steel corrugated-plate walls with T-section (T-CDSCWs) under axial compression and biaxial bending. T-CDSCWs are composed of flange and web walls and boundary elements. The T-section is mono-symmetric and exhibits different interaction curves of load-carrying capacity when subjected to axial load and different direction bending. Based on the finite element (FE) model established by the previous study, the local buckling of the steel corrugated-plates is considered in the load-carrying capacity. Subsequently, this paper investigates the behaviours of T-CDSCWs under axial compression and uniaxial bending, including stress distribution, load–displacement curves, and interaction curves. Based on the numerical results, the pure moment capacity is found to be evaluated by reducing the plastic moment capacity, and the interaction equations of N –positive M x , N –negative M x , and N – M y are proposed in the bilinear, linear, and parabolic form. For biaxial bending, the shape of the interaction curves is almost exclusively related to the axis compression ratio. Accordingly, this paper proposes the interaction equations of M x – M y subjected to certain axial compression. Moreover, the local buckling of steel corrugated-plates has no significant influence on the shape of the interaction curves no matter the bending direction. The global stability of T-CDSCWs is not involved in the study, and with the interaction equations obtained above, the global stability design of T-CDSCWs can be investigated by introducing the magnification factor of the bending moment caused by the secondary effect. [ABSTRACT FROM AUTHOR]